Primary channel selection method for relay networks

ABSTRACT

The primary channel selection method for relay networks functions in a relaying cognitive network where a number of relays are used to forward the source message to destination. The primary users utilize orthogonal spectrum bands. One primary user is selected among the available primary users in order to share its spectrum with the secondary users (source and relay). A certain amount of interference is allowed between the primary and secondary users when the primary users&#39; channels are shared by the secondary users.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to the use of orthogonal spectrum bands incellular networks, and particularly to a primary channel selectionmethod for relay networks where primary users utilize orthogonalspectrum bands to improve secondary user (SU) performance.

2. Description of the Related Art

In a decode-and-forward (DF) relay scheme primary user (PU) receiversare generally not deemed to use orthogonal spectra, i.e., cognitiverelay networks (CRNs) with multiple primary user (PU) receivers operatewith PU receivers utilizing the same spectrum band. This usage scheme ofthe PU receivers in the context of an opportunistic DF relay cognitivenetwork is to the detriment of the quality of reception of the secondaryuser (SU) receivers.

Thus, a primary channel selection method for relay networks solving theaforementioned problems is desired.

SUMMARY OF THE INVENTION

The primary channel selection method for relay networks functions in arelaying cognitive network where a number of relays are used to forwardthe source message to destination. The primary users utilize orthogonalspectrum bands. One primary user is selected among the available primaryusers in order to share its spectrum with the secondary users (sourceand relay). A certain amount of interference is allowed between theprimary and secondary users when the primary users' channels are sharedby the secondary users.

These and other features of the present invention will become readilyapparent upon further review of the following specification anddrawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram showing a cognitive opportunistic DF(decode and forward) relay network with interference and multiple PU(primary user) receivers used in a primary channel selection method forrelay networks according to the present invention.

FIG. 2 is a plot showing outage probability vs SNR (signal to noiseratio) of cognitive opportunistic DF relay network with interference andmultiple PU receivers for different values of K.

FIG. 3 is a plot showing outage probability vs SNR of cognitiveopportunistic DF relay network with interference and multiple PUreceivers for different values of M.

FIG. 4 is a plot showing outage probability vs out of cognitiveopportunistic DF relay network with interference and multiple PUreceivers for a first set of values of γ _(r) ^(I) and γ _(d) ^(I).

FIG. 5 is a plot showing outage probability vs SNR of cognitiveopportunistic DF relay network with interference and multiple PUreceivers for a second set of values of γ_(out).

FIG. 6 is a plot showing outage probability vs SNR of cognitiveopportunistic DF relay network with interference and multiple PUreceivers for different values of γ _(r) ^(I), γ _(d) ^(I) and M.

FIG. 7 is a plot showing outage probability vs SNR of cognitiveopportunistic DF relay network with interference and multiple PUreceivers for a third set of values of γ _(r) ^(I) and γ _(d) ^(I).

FIG. 8 is a plot showing outage probability Outage probability vs M ofcognitive opportunistic DF relay network with interference and multiplePU receivers for a set of values of K.

FIG. 9 is a block diagram showing a possible architecture of a cognitiveradio using the primary channel selection method for relay networksaccording to the invention.

Similar reference characters denote corresponding features consistentlythroughout the attached drawings.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The primary channel selection method for relay networks functions in arelaying cognitive network where a number of relays are used to forwardthe source message to destination. The primary users utilize orthogonalspectrum bands, thus the present primary channel selection methodprovides opportunistic DF CRNs with multiple PU receivers usingorthogonal spectrum bands. One primary user is selected among theavailable primary users in order to share its spectrum with thesecondary users (source and relay). A certain amount of interference isallowed between the primary and secondary users when the primary users'channels are shared by the secondary users. Using orthogonal spectrumbands in cellular networks reduces the interference between users in thesame way that downlink transmissions using orthogonal frequency bandsare used by base stations in transmitting data for different users. Theprimary channel selection method for relay networks spans a secondarysource, multiple secondary relays, a secondary destination, a primarytransmitter and multiple primary receivers, and involves selection of aprimary receiver out of the available primary receivers in such a way asto enhance the performance of the secondary system.

As shown in FIG. 1, a dual-hop spectrum-sharing relay network 100includes one secondary user (SU) source S 103, K DF SU relays R_(k) 108(k=1, . . . , K), one SU destination D 106, M primary user (PU)receivers P_(m) 102 (m=1, . . . , M) using orthogonal frequency bands,and one PU transmitter P_(Tx) 104. All nodes are assumed to be equippedwith single antenna and the communication is assumed to operate in ahalf-duplex mode. Also, a downlink transmission is assumed to beconducted between the PU transmitter 104 or base station and its PUreceivers 102. The SU users need to share the spectrum with the PUreceiver whose channel results in a best performance for the secondarysystem. At the same time, the K SU relays 108 and destination 106 willbe corrupted by interference from the PU transmitter or base station 104P_(Tx). The direct link is assumed to be in a deep fade and hence, it isneglected in the analysis. The communications take place in two phases.In the first phase, the SU source 103 sends its message x to K relaysunder a transmit power constraint which guarantees that the interferencewith the selected PU receiver P_(Scl) does not exceed a threshold I_(p).To satisfy the PU interference constraint and result in a bestperformance for the secondary system, the SU source S 103 must transmitat a power given by

${P_{s} = {{I_{p}/\begin{matrix}\min \\m\end{matrix}}{g_{s,m}}^{2}}},$

where g_(s,m) is the channel coefficient of the S→P_(m) link. Thereceived signal at the k^(th) relay can be expressed as:

γ_(S,k)=√{square root over (P _(S))}h _(S,k) x ₀+√{square root over (P_(p) ¹)}f _(p,k) x _(p) +n _(k),  (1)

where h_(S,k) is the channel coefficient of the S→R_(k) link, x₀ is thetransmitted symbol from the SU source S with

{|x₀|²}=P₀, f_(p,k) is the channel coefficient of the P_(Tx)→R_(k) link,x_(p) is the transmitted symbol from the PU transmitter P_(Tx) with

{|x_(p)|₂}=P_(p) ¹, where the superscript 1 is used to denote that thisis the transmitted power at the first communication phase, n_(k)˜

(0, N₀) is an additive white Gaussian noise (AWON), and

{•} denotes the expectation operation. The variables h_(k,d), g_(k,m),and f_(p,d) are defined as the channel coefficients of the R_(k)→D,R_(k)→P_(m), P_(Tx)→D links, respectively. All channel coefficients areassumed to follow the Rayleigh distribution, that is, the channel powersdenoted by |g_(s,m)|², |h_(S,k)|², |h_(k,d)|², |g_(k,m)|², |f_(p,k)|²,and |f_(p,d)|² are exponentially distributed random variables (RVs) withmean powers μ_(s,m), Ω_(s,k), Ω_(k,d), μ_(k,m), β_(p,k), and β_(p,d),respectively. Using (1), the signal-to-interference-plus-noise ratio(SINR) at the k^(th) relay can be written as:

$\begin{matrix}{{\gamma_{s,k} = {\frac{\frac{I_{p}}{N_{O}}\frac{{h_{s,k}}^{2}}{W_{1}}}{{\frac{P_{p}^{1}}{N_{O}}{f_{p,k}}^{2}} + 1} = {\frac{X_{s,k}}{Y_{1} + 1} = \frac{X_{s,k}}{Z_{1}}}}},} & (2)\end{matrix}$

where

${W_{1} = {\begin{matrix}\min \\m\end{matrix}{g_{s,m}}^{2}}},$

X_(S,k), Y₁, and Z₁ are some RVs used herein. Let C_(L) denote adecoding set defined by the set of active relays that could havecorrectly decoded the source message in first phase of communication. Itis defined as:

$\begin{matrix}\begin{matrix}{{C_{L}\overset{\Delta}{=}\left\{ {k \in {{S_{r}\text{:}\mspace{14mu} \frac{1}{2}{\log_{2}\left( {1 + \gamma_{S,k}} \right)}} \geq R}} \right\}},} \\{{= \left\{ {k \in {{S_{r}\text{:}\mspace{14mu} \gamma_{S,k}} \geq {2^{2R} - 1}}} \right\}},}\end{matrix} & (3)\end{matrix}$

where S_(r) is a set of L relays and R denotes a fixed spectralefficiency threshold.

In the second phase and after decoding the received message, a relaywith the best second hop channel's SNR is selected from C_(L) to forwardthe re-encoded copy of the SU source message to the SU destination. Inorder to satisfy the PU interference constraint and result in a bestperformance for the secondary system, the transmit power at R_(t) mustbe

$P_{R_{l}} = {{I_{p}/\begin{matrix}\min \\m\end{matrix}}{{g_{l,m}}^{2}.}}$

The SINR at the destination resulting from the l^(th) relay signal canbe written as:

$\begin{matrix}{{\gamma_{l,d} = {\frac{\frac{I_{p}}{N_{O}}\frac{{h_{l,d}}^{2}}{W_{2}}}{{\frac{P_{p}^{2}}{N_{O}}{f_{p,d}}^{2}} + 1} = {\frac{X_{l,d}}{Y_{2} + 1} = \frac{X_{l,d}}{Z_{2}}}}},} & (4)\end{matrix}$

where P_(p) ² is the transmitted power of the interferer at the secondcommunication phase,

${W_{2} = {\begin{matrix}\min \\m\end{matrix}{g_{l,m}}^{2}X_{l,d}}},$

Y₂, and Z₂ are some RVs used herein. Equivalently, the relay with thebest X_(t,d) is selected to forward the source signal to destination,since the denominator is common to the SINRs from all relays belongingto C_(L).

According to the present primary channel selection method for relaynetworks, at the beginning of first communication phase, the SU sourceobtains the channel information of the PU receivers (g_(s,m), m=1, . . ., M), by either a direct reception of pilot signals from primary usersor by exchange of channel information between primary and secondaryusers through a band manager. Using the estimated channels, the SUsource knows which spectrum band to share with the PU and determines itstransmit power using

$P_{s} = {{I_{p}/\begin{matrix}\min \\m\end{matrix}}{{g_{s,m}}^{2}.}}$

Then, the SU source sends its message to the K SU relays through whicheach relay calculates its first hop SINR (γ_(S,k), k=1, . . . , K) using(2) and then compares it with the outage threshold γ_(out). The relayswhose SINRs are greater than γ_(out) are called active relays. At thebeginning of second communication phase and through sensing of pilotsignals from PU receivers, the active relays obtain the channelinformation of their links with primary receivers (g_(k,m), k=1, . . . ,L; m=1, . . . , M). Using the estimated channels, each active relayknows which spectrum band to share with the PU and determines itstransmit power using

$P_{R_{l}} = {{I_{p}/\begin{matrix}\min \\m\end{matrix}}{{g_{l,m}}^{2}.}}$

Then, each active relay sends a training sequence to the SU destinationthrough which the SU destination calculates the signal-to-noise ratio(SNR) received from the relays (X_(l,d), l=1, . . . , L). To avoidinterference between relays while transmitting their training sequences,they can be coordinated to transmit in a time-division duplex manner.This is a feasible assumption in TDMA systems. Using the calculated SNRsand according to the opportunistic relay selection criterion, thedestination sends a positive acknowledge or a 1-bit feedback to therelay who has the largest SNR asking him to start forwarding are-encoded version of the source message to it. The interferencechannels at the relays may be locally estimated by the relay nodes as astep in decoding the source message before it is being forwarded to thedestination. This helps in calculating the SINRs (γ_(S,k), k=1, . . . ,K) of the relays to compare with the outage threshold γ_(out) whenfinding the set of active relays C_(L). The relay selection in thesecond hop is performed using the numerators of SINRs received at thedestination from the active relays (X_(l,d), l=1, . . . , L). This isbecause the interference at the destination is common to the SNRs of allrelays belonging to C_(L). Also assume that the channels of the secondhop transmission do not change while a decision on which relay isselected is made. Using the calculated SNRs and according to theopportunistic relay selection criterion, the destination sends apositive acknowledge or a 1-bit feedback to the relay who has thelargest SNR asking him to start forwarding a re-encoded version of thesource message to it. Steps of the proposed PU receiver selectionprotocol are detailed in Table 1.

TABLE 1 PU Receiver Selection Protocol Steps STEP Function  1 SU sourceestimates (g_(s,m), m = 1, . . . , M)  2 $\begin{matrix}{{SU}\mspace{14mu} {source}\mspace{14mu} {calculates}} \\{P_{s} = {{I_{p}/\begin{matrix}\min \\m\end{matrix}}{g_{s,m}}^{2}}} \\{{and}\mspace{14mu} {sends}\mspace{14mu} {its}\mspace{14mu} {message}\mspace{14mu} {to}} \\{K\mspace{14mu} {relays}}\end{matrix}\quad$  3 Relays calculate (γ_(S,k), k = 1, . . . , K)  4Test γ_(S,j) until γ_(S,j) ≧ γ_(out)  5 R_(j) ∈ D_(L)  6 Test for theK^(th) relay j = K?  7 The relays in C_(L) estimate g_(l,m) for l = 1, .. . , L; m = 1, . . . , M  8 $\begin{matrix}{{Each}\mspace{14mu} {relay}\mspace{14mu} {in}\mspace{14mu} C_{L}} \\{{{calculates}\mspace{14mu} P_{l}} =} \\{{I_{p}/\begin{matrix}\min \\m\end{matrix}}{g_{l,m}}^{2}\mspace{14mu} {and}\mspace{14mu} {sends}\mspace{14mu} a} \\{{training}\mspace{14mu} {sequence}\mspace{14mu} {to}\mspace{14mu} {SU}} \\{destination}\end{matrix}{\quad\quad}$  9 SU destination calculates X_(l,d) andsends positive ACK to relay of max. X_(l,d) 10 The relay of max. X_(l,d)starts forwarding SU source message to SU destination

With respect to exact closed-form expressions for the outage probabilityof the studied system for the independent non-identically distributed(i.n.i.d.) generic case of relay second hop channels, the outageprobability is defined as the probability that the SINR at D goes belowa predetermined outage threshold γ_(out), i.e.,P_(out)=P_(r)[γ_(D)<γ_(out)] where P_(r)[.]denotes the probabilityoperation. Let C_(L) be a decoding subset with a number of L activerelays (i.e., cardinality |C_(L)|=L), then:

$\begin{matrix}{{{P_{r}\left\lbrack C_{L} \right\rbrack} = {\prod\limits_{l \in C_{L}}\; {{P_{r}\left\lbrack {\gamma_{S,l} \geq u} \right\rbrack}{\sum\limits_{m \notin C_{L}}\; {P_{r}\left\lbrack {\gamma_{S,m} < u} \right\rbrack}}}}},} & (5)\end{matrix}$

where u=(2^(2R)−1). The outage probability for the studied system can bewritten as

$\begin{matrix}\begin{matrix}{P_{out}\overset{\Delta}{=}{P_{r}\left\lbrack {{\frac{1}{2}{\log_{2}\left( {1 + \gamma_{D}} \right)}} < R} \right\rbrack}} \\{{= {\sum\limits_{L = 0}^{K}\; {\sum\limits_{C_{L}}\; {{P_{r}\left\lbrack {{\gamma_{D} < u}C_{L}} \right\rbrack}{P_{r}\left\lbrack C_{L} \right\rbrack}}}}},}\end{matrix} & (6)\end{matrix}$

where the internal summation is taken over all of

$\quad\begin{pmatrix}K \\L\end{pmatrix}$

possible subsets of size L from the set with the K relays. In order toevaluate (6), P_(r) [γ_(D)<u|C_(L)] and P_(r)[C_(L)] are first derived.The term P_(r)[C_(L)] is obtained by first deriving the CDF of γ_(S,k).This CDF conditioned on W₁ can be obtained using:

$\begin{matrix}{{P_{r}\left\lbrack {{\gamma_{S,k} < u}W_{1}} \right\rbrack} = {\int_{1}^{\infty}{{{fZ}_{1}(z)}\underset{\underset{{FX}_{s,k}{({{uz}W_{1}})}}{}}{\int_{0}^{uz}{{{fX}_{s,k}\left( {xW_{1}} \right)}\ {x}\ {{z}.}}}}}} & (7)\end{matrix}$

The probability density function (PDF) of Z₁ can be directly obtainedfrom the PDF of Y₁ which is given for Rayleigh fading channels as

${{f_{Y_{1}}(y)} = {{\alpha_{p,k}{\exp \left( {\alpha_{p,k}y} \right)}\mspace{14mu} {where}\mspace{14mu} \alpha_{p,k}} = \left( {\gamma_{r}^{- I}\beta_{p,k}} \right)^{- 1}}},{{{where}\mspace{14mu} \gamma_{r}^{- I}} = {\frac{P_{p}^{1}}{N_{O}}.}}$

Using transformation of RVs, the PDF of Z₁ can be easily obtained asf_(Z) ₁ (z)=α_(p,k)exp(−α_(p,k))exp(−α_(p,k)z). The CDF of X_(s,k)conditioned on W₁ can be obtained as:

$\begin{matrix}{{{{F_{X_{s,k}}\left( {xW_{1}} \right)} = {1 - {\exp \left( {{- \lambda_{s,k}}W_{1}x} \right)}}},{where}}{\lambda_{s,k} = {1/{\left( {\Omega_{s,k}\frac{I_{p}}{N_{o}}} \right).}}}} & (8)\end{matrix}$

Upon substituting f_(Z) ₁ (z) and (8) in (7) and after doing theintegration, the result is:

$\begin{matrix}{{P_{r}\left\lbrack {{\gamma_{s,k} < u}W_{1}} \right\rbrack} = {1 - {\alpha_{p,k}{\frac{\exp \left( {- \left( {\lambda_{s,k}W_{1}u} \right)} \right)}{\left( {\left( {\lambda_{s,k}W_{1}u} \right) + \alpha_{p,k}} \right)}.}}}} & (9)\end{matrix}$

Assuming i.n.i.d channels between the SU source and the PU receivers,the CDF and PDF of W₁ are respectively given by:

$\begin{matrix}{\begin{matrix}{{F_{W_{1}}(w)} = {1 - {\prod\limits_{m = 1}^{M}\left( {1 - {F_{{g_{s,m}}^{2}}(w)}} \right)}}} \\{= {1 - {\exp \left( {\sum\limits_{m = 1}^{M}{\varsigma_{s,m}w}} \right)}}}\end{matrix}\quad} & (10) \\{{{f_{W_{1}}(w)} = {\sum\limits_{m = 1}^{M}{\varsigma_{s,m}{\exp \left( {- {\sum\limits_{m = 1}^{M}{\varsigma_{s,m}w}}} \right)}}}},} & \;\end{matrix}$

where ç_(s,m)=1/μ_(s,m). Now, averaging over the PDF of W₁ using ∫₀^(∞)P_(r) [γ_(S,k)<u|W₁]f_(W) ₁ (w)dw, the following relation isobtained:

$\begin{matrix}{{{P_{r}\left\lbrack {\gamma_{s,k} < u} \right\rbrack} = {1 + \alpha_{p,k}}},{\left( \frac{\sum\limits_{m = 1}^{M}\varsigma_{s,m}}{\lambda_{s,k}} \right){\exp\left( {\alpha_{p,k}\left( {1 + \frac{\sum\limits_{m = 1}^{M}\varsigma_{s,m}}{\lambda_{s,k}u}} \right)} \right)}E\; {\left( {- {\alpha_{p,k}\left( {1 + \frac{\sum\limits_{m = 1}^{M}\varsigma_{s,m}}{\lambda_{s,k}u}} \right)}} \right)}u^{- 1}},} & (11)\end{matrix}$

where Ei(•) is an Exponential integral. Upon substituting (11) in (5),the term P_(r)[C_(L)] can be calculated. The second term in (6) isderived which is P_(r)[γ_(D)<u|C_(L)]. With opportunistic or best-relayselection scheme, the CDF of γ_(D) conditioned on C_(L), W₂ can beobtained using:

$\begin{matrix}{{P_{r}\left\lbrack {{{\gamma_{D} < u}C_{L}},W_{2}} \right\rbrack} = {\int_{1}^{\infty}{{f_{Z_{2}}\ (z)}\underset{\underset{F_{X_{sel}}{({{uz}W_{2}})}}{}}{\int_{0}^{uz}{{f_{X_{sel}}\left( {xW_{2}} \right)}\ {x}{z}}}}}} & (12)\end{matrix}$

where f_(X) _(sel) (x|W₂) is the PDF of the best relay conditioned onW₂. The PDF of Z₂ can be directly obtained from the PDF of Y₂ which isgiven for Rayleigh fading channels as:

f _(Y) ₂ (y)=α_(p,d)exp(−α_(p,d) y), where α_(p,d)=(γ_(d)^(I)β_(p,d))⁻¹,

where

${\overset{\_}{\gamma}}_{d}^{I} = {\frac{P_{p}^{1}}{N_{o}}.}$

Using transformation of RVs, the PDF of Z₂ can be easily obtained as fZ₂(z)=α_(p,d)exp(−α_(p,d))exp(−α_(p,d)z). The CDF of X_(Sel) conditionedon W₂ can be written as:

F _(X) _(sel) (x|W ₂)=Π_(l=1) ^(L) F _(l,d)(x|W ₂),  (13)

where F_(l,d) (x|W₂) is given by:

F _(X) _(l,d) (x|W ₂)=1−exp(−λ_(l,d) W ₂ x),  (14)

where

$\lambda_{l,d} = {1/{\left( {\Omega_{l,d}\frac{I_{p}}{N_{O}}} \right).}}$

Upon substituting (14) in (13), and applying the identity:

$\begin{matrix}{{{\prod\limits_{l = 1}^{L}\; \left( {1 - q_{l}} \right)} = {\sum\limits_{l = 0}^{L}{\frac{\left( {- 1} \right)^{l}}{l!}{\sum\limits_{n_{1},\ldots \mspace{14mu},n_{l}}^{L}{\prod\limits_{t = 1}^{l}\; q_{n_{t}}}}}}},} & (15)\end{matrix}$

with Σ_(n) ₁ _(, . . . , n) _(l) ^(L) being a short hand-notation for

$\begin{matrix}{{{\sum{\ldots {\sum n_{1}}}} = {\ldots = {n_{l} = 1}}},{n_{1} \neq \ldots \neq n_{l}}} & (13)\end{matrix}$

can be rewritten as:

$\begin{matrix}{{F_{X_{sel}}\left( {xW_{2}} \right)} = {\sum\limits_{l = 0}^{L}{\frac{\left( {- 1} \right)^{l}}{l!}{\sum\limits_{n_{1},\ldots \mspace{14mu},n_{l}}^{L}{\prod\limits_{t = 1}^{l}{{\exp \left( {{- \lambda_{n_{t},d}}W_{2}x} \right)}.}}}}}} & (16)\end{matrix}$

Upon substituting (16) in (12), and after simple manipulations, thefollowing relation is obtained:

$\begin{matrix}{{P_{r}\left\lbrack {{{\gamma_{D} < u}C_{L}},W_{2}} \right\rbrack} = {\alpha_{p,d}{\sum\limits_{l = 0}^{L}{\frac{\left( {- 1} \right)^{l}}{l!}{\sum\limits_{n_{1},\ldots \mspace{14mu},n_{l}}^{L}{\prod\limits_{t = 1}^{l}{\frac{\exp \left( {{- \lambda_{n_{t}d}},{W_{2}x}} \right)}{\left( {{\lambda_{n_{t},d}W_{2}u} + \alpha_{p,d}} \right)}.}}}}}}} & (17)\end{matrix}$

Assuming i.n.i.d channels between the SU relays and the PU receivers,the CDF and PDF of W₂ are respectively given by:

$\begin{matrix}{\begin{matrix}{{F_{W_{2}}(w)} = {1 - {\prod\limits_{m = 1}^{M}\left( {1 - {F_{{g_{n_{t},m}}^{2}}(w)}} \right)}}} \\{= {1 - {\exp \left( {\sum\limits_{m = 1}^{M}{\varsigma_{n_{t},m}w}} \right)}}}\end{matrix}\quad} & (18) \\{{{f_{W_{2}}(w)} = {\sum\limits_{m = 1}^{M}{\varsigma_{n_{t},m}{\exp \left( {- {\sum\limits_{m = 1}^{M}{\varsigma_{n_{t},m}w}}} \right)}}}},} & \;\end{matrix}$

where ç_(n) _(t) _(,m)=1/μ_(n) _(t) _(,m) Averaging over the PDF of W₂using:

∫₀ ^(∞) P _(r)[γ_(D) <u|C _(L) ,W ₁ ]f _(W) ₁ (w)dw,

the following relation is obtained:

$\begin{matrix}{{P_{r}\left\lbrack {{\gamma_{D} < u}C_{L}} \right\rbrack} = {{- \alpha_{p,d}}{\sum\limits_{l = 0}^{L}{\frac{\left( {- 1} \right)^{l}}{l!}{\sum\limits_{n_{1},\ldots \mspace{14mu},n_{l}}^{L}{\prod\limits_{t = 1}^{l}{\left( \frac{\sum\limits_{m = 1}^{M}\varsigma_{s,m}}{\lambda_{n_{t},d}} \right){\exp \left( \frac{\sum\limits_{m = 1}^{M}\varsigma_{n_{t},m}}{\lambda_{n_{t},d}u} \right)} \times E\; {\left( \frac{\sum\limits_{m = 1}^{M}{\varsigma_{n_{t},,m}\alpha_{p,d}}}{\lambda_{n_{t},d}u} \right)}u^{- 1}}}}}}}} & (19)\end{matrix}$

Having the terms P_(r)[C_(L)], P_(r)[γ_(D)<u|C_(L)] being obtain, aclosed-form expression for the outage probability in (6) can beachieved.

Due to complexity of the achieved expressions in previous sections, itis hard to get more insights about system performance. Therefore, we seeit is important to derive simple expressions where more insights aboutthe system behavior can be achieved.

At high SNR values, the outage probability can be expressed asP_(out)≈(G_(c)SNR)^(−G) ^(d) , where G_(c) denotes the coding gain ofthe system and G_(d) is the diversity order of the system. The relaysare assumed to have identical second hop channels (X_(l,d), l=1, . . . ,L) and identical, R→P_(m) links (γ_(S,k), k=1, . . . , K) and (γ_(S,k),k=1, . . . , K). Also, the channels between the SU source and PUreceivers S→P_(m) are assumed to be identical (γ_(S,k), k=1, . . . , K).As

$\left. \frac{I_{p}}{N_{o}}\rightarrow\infty \right.,$

the CDF in (8) simplifies to F_(X) _(S,k) (x|W₁)≈λ_(S,k) W₁x. Uponsubstituting this CDF in (7) the CDF P_(r) [γ_(S,k)<u] which is a partof the term P_(r)[C_(L)] can be obtained at high SNR values as:

$\begin{matrix}{{P_{r}\left\lbrack {\gamma_{s,k} < u} \right\rbrack} \approx {\frac{\exp \left( \alpha_{p,k} \right)}{\alpha_{p,k}}\left( \frac{\lambda_{s,k}}{M\; \varsigma_{s,p}} \right){r\left( {2,\alpha_{p,k}} \right)}{u.}}} & (20)\end{matrix}$

In evaluating P_(r)[γ_(r,d)<u|C_(L)], as

$\left. \frac{I_{p}}{N_{O}}\rightarrow\infty \right.,$

the CDF in (14) simplifies for the identical case to F_(X) _(r,d)(x|W₂)≈λ_(r,d)W_(2γ). Upon substituting this CDF in (12) the termP_(r)[γ_(r,d)<u|C_(L)] can be obtained at high SNR as:

$\begin{matrix}{{P_{r}\left\lbrack {{\gamma_{r,d} < u}C_{L}} \right\rbrack} \approx {{L!}\left( \alpha_{p,d} \right)^{- L}\left( \frac{\lambda_{r,d}}{M\; \varsigma_{r,p}} \right)^{L}{u^{L}.}}} & (21)\end{matrix}$

The transmit power of the PU transmitter can be assumed to be fixed orit can be assumed to be dependent of and scaling with the transmit powerof the SU transmitters. In practice, the network where the interferencepower scales with the desired user power is called symmetric network;whereas, the network where the interference power is fixed and notrelated to the desired user power is called asymmetric network. Thesetwo cases are considered in the following analysis.

Where γ _(r) ^(I), γ _(d) ^(I) are constants (asymmetric network), theoutage probability for this case is dominated by the first term in (6)which was obtained in (21). For this case, the parameter α_(p,d) can beapproximated by α_(p,d)≈(γ _(d) ^(I)β_(p,d))⁻¹. For the identical case

$\lambda_{r,d} = {1/{\left( {\Omega_{r,d}\frac{I_{p}}{N_{O}}} \right).}}$

Hence, the outage probability at high SNR values can be obtained in asimple expression as:

$\begin{matrix}{P_{out}^{\infty} = {\left\lbrack {\left( {L!} \right)^{{- 1}/L}\left( {\frac{{\overset{\_}{\gamma}}_{d}^{I}\beta_{f_{p,d}}M\; \varsigma_{s,p}\Omega_{r,d}}{\gamma_{out}}\frac{I_{p}}{N_{0}}} \right)} \right\rbrack^{- L}.}} & (22)\end{matrix}$

As can be seen from (22), the coding gain of the system is affected bythe parameters γ _(d) ^(I), β_(p,d), M, ç_(s,p), Ω_(r,d), and γ_(out)while the diversity order equals the number of active relays L. Themaximum number of active relays in DF relay networks could reach thetotal number of relays K and this makes the diversity order of thesystem in (22) equal K. Furthermore, it can be noticed from (22) thatthe diversity order of cognitive opportunistic DF relay networks withpartial-relay selection is the same as that of its non-cognitivecounterpart and is independent of the primary cell. With fixedinterference power, the interference from primary users will bedegrading the performance of the secondary users through affecting thecoding gain without affecting the diversity order.

In the second case where γ _(r) ^(I), γ _(d) ^(I) are scaling with SNR(symmetric network) the interference powers can be expressed as

${{\overset{\_}{\gamma}}_{r}^{I} = {a\frac{I_{p}}{N_{O}}}},{{\overset{\_}{\gamma}}_{d}^{I} = {b\frac{I_{p}}{N_{O}}}},$

where a, b are some positive numbers. As the interference at the relaysdiffers than that at the destination, we have the following differentsubcases;

${\overset{\_}{\gamma}}_{r}^{I} = {{a\frac{I_{p}}{N_{O}}\mspace{14mu} {or}\mspace{14mu} {\overset{\_}{\gamma}}_{d}^{I}} = {{b\frac{I_{p}}{N_{O}}\mspace{14mu} {or}\mspace{14mu} {\overset{\_}{\gamma}}_{r}^{I}} = {{a\frac{I_{p}}{N_{O}}\mspace{14mu} {and}\mspace{14mu} {\overset{\_}{\gamma}}_{d}^{I}} = {b{\frac{I_{p}}{N_{O}}.}}}}}$

With

${\overset{\_}{\gamma}}_{r}^{I} = {a\frac{I_{p}}{N_{O}}}$

and fixed γ _(d) ^(I), the outage probability for this case is dominatedby the second term in (6) which was obtained in (20). Also, theparameter α_(p,r) can be approximated by

${\alpha_{p,r} \approx \left( {{\overset{\_}{\gamma}}_{r}^{I}\beta_{p,r}} \right)^{- 1}} = {\left( {a\frac{I_{p}}{N_{O}}\beta_{p,r}} \right)^{- 1}.}$

For the identical case, we have

$\lambda_{s,r} = {1/{\left( {\Omega_{s,r}\frac{I_{p}}{N_{O}}} \right).}}$

Hence, the outage probability at high SNR values can be obtained in asimple expression as:

$\begin{matrix}\begin{matrix}{P_{out}^{\infty} = {\left( {a\frac{I_{p}}{N_{O}}\beta_{p,r}} \right){\exp \left( {{1/a}\frac{I_{p}}{N_{O}}\beta_{p,r}} \right)}\left( \frac{\gamma_{s,k}\frac{I_{p}}{N_{O}}}{M\; \varsigma_{s,p}} \right)^{- 1}{r\left( {2,{{1/a}\frac{I_{p}}{N_{O}}\beta_{p,r}}} \right)}\gamma_{out}}} \\{= {\left( {a\; \beta_{p,r}} \right)\left( {{\Omega_{s,r}/M}\; \mu_{s,p}} \right)^{- 1}\gamma_{out}}}\end{matrix} & (23)\end{matrix}$

where at high SNR, the exponential term and the incomplete Gammafunction term in the first line of (23) reach the value of 1. As can beseen from (23), when the interference at the relays has a power thatscales with SNR, the diversity gain of the system reaches zero and anoise floor is expected to appear in the results. In such case, thesystem performance is affected by various parameters, such as β_(p,r),Ω_(s,r), M, μ_(s,p), and γ_(out).

When the interference at the destination scales with SNR

${\overset{\_}{\gamma}}_{d}^{I} = {b\frac{I_{p}}{N_{O}}}$

and the interference at the relays has a fixed power, the outageprobability for this case is dominated by the first term in (6) whichwas obtained in (21). Also, the parameter

${\alpha_{p,d} \approx \left( {{\overset{\_}{\gamma}}_{d}^{I}\beta_{p,d}} \right)^{- 1}} = {\left( {b\frac{I_{p}}{N_{O}}\beta_{p,d}} \right)^{- 1}.}$

For the identical case, we have

$\lambda_{r,d} = {1/{\left( {\Omega_{r,d}\frac{I_{p}}{N_{O}}} \right).}}$

Hence, the outage probability at high SNR values can be obtained in asimple expression as:

$\begin{matrix}{P_{out}^{\infty} = {\left\lbrack {\left( {L!} \right)^{{- 1}/L}\left( \frac{{\overset{\_}{\gamma}}_{d}^{I}\beta_{p,d}M\; \varsigma_{r,p}\Omega_{r,d}}{\gamma_{out}} \right)} \right\rbrack^{- L}.}} & (24)\end{matrix}$

It is clear from (24) that when the interference at the destination hasa power that scales with SNR, the system achieves a diversity gain ofzero and the system performance is affected by various parametersincluding L, γ _(d) ^(I), β_(p,d), M, ç_(r,p), Ω_(r,d), and γ_(out).

Finally, when the interference at the relays and the interference at thedestination have powers that scale with SNR

${{\overset{\_}{\gamma}}_{r}^{I} = {a\frac{I_{p}}{N_{O}}}},{{\overset{\_}{\gamma}}_{d}^{I} = {b\frac{I_{p}}{N_{O}}}},$

the outage probability for this case was shown to be dominated by thesecond term in (6) which was obtained in (20). Therefore, the outageprobability for this case is similar to that found in (23) where thediversity gain reaches zero and the system behavior is affected byseveral parameters including β_(p,r), M, μ_(s,p), Ω_(s,r), and γ_(out).

The present primary channel selection method for relay networks may beimplemented in cognitive radios such as for example, without limitationtransceiver 900 (shown in FIG. 9) which comprises transmitter 901,receiver 903, controller 905, channel status database 907, memory 919,user interface 921, power module 927, and interference measurementmodule 935. In the embodiment, transceiver 900 receives and transmitsinformation in a network such as network 100 illustrated in FIG. 1. Inthe aforementioned half-duplex operation receiver 903 and transmitter901 share antenna 931 in a manner that may support half-duplexoperation. The PU receiver selection protocol steps detailed above andoutlined in Table 1 may be performed by controller 905 in operablecommunication with memory 919, channel status database 907, interferencemeasurement module 935 receiver 903 and transmitter 901. For example,controller 905 may process the data received by receiver 903 andtransmitted by transmitter 901.

The cognitive information required to implement the primary channelselection method for relay networks may be stored in the channel statusdatabase 907. Additionally, the controller may determine interferencelevels, as measured by interference measurement module 935 to assist inthe channel estimations required by the present primary channelselection method. Transceiver 900 may share information about themeasured interference levels with other transceivers in network 100(shown in FIG. 1).

Memory 919 may also store instructions for controller 905 to executesteps of the present primary channel selection method for relaynetworks. User interface 921 enables a user to operate the cognitiveradio while power unit 927 allows the other components of cognitiveradio 900 to be energized.

It should be understood by one of ordinary skill in the art that thecognitive radio 900 presented in FIG. 9 is exemplary only and that thepresent method can comprise software or firmware code executing on acomputer, a microcontroller, a microprocessor, or a DSP processor, statemachines implemented in application specific or programmable logic; ornumerous other forms without departing from the spirit and scope of theinvention. The present method can be provided as a computer program,which includes a non-transitory machine-readable medium having storedthereon instructions that can be used to program a computer (or otherelectronic devices) to perform a process according to the method. Themachine-readable medium can include, but is not limited to, floppydiskettes, optical disks, CD-ROMs, and magneto-optical disks, ROMs,RAMs, EPROMs, EEPROMs, magnetic or optical cards, flash memory, or othertype of media or machine-readable medium suitable for storing electronicinstructions.

With respect to validation of the achieved analytical and asymptoticexpressions, comparison metrics were compiled using Monte-Carlosimulations. Some numerical examples are provided to show the effect ofthe interference and some system parameters such as number of relays andnumber of PU receivers on the system performance.

Plot 200 of FIG. 2 portrays the outage performance versus SNR fordifferent numbers of relays K, and demonstrates that perfect fittingexists between the analytical and asytnptotic results with Monte-Carlosimulations. Also, plot 200 demonstrates that with constant interferencepower, as K increases, the diversity order of the system increases andthe system performance enhances. This is clear from the asymptoticresults where the diversity order equals K when the interference poweris fixed. Moreover, as shown in FIG. 2, the system can still achievefull diversity gain as SNR increases.

The effect of number of PU receivers M on the system performance isstudied in plot 300 of FIG. 3. Again, the perfect fitting between theanalytical results and asymptotic results is clear in plot 300. Moreimportantly, plot 300 shows that as M increases, better the achievedperformance. This is because having more PU receivers increases theprobability to find primary receivers of weak channels and hence, higherthe transmit power of the SU transmitters. Furthermore, plot 300 showsthat the number of PU receivers affects the system performance throughaffecting its coding gain and not the diversity order. Again, this factwas proved by the asymptotic results.

Plot 400 of FIG. 4 illustrates the interference effect on the systemperformance. It portrays the outage behavior versus outage thresholdγ_(out) for different values of interference powers γ _(r) ^(I), γ _(d)^(I) when they are equal. As expected, as γ _(r) ^(I), γ _(d) ^(I)increase, the achieved performance gets worse. Also, the continuousincrease in γ_(out) results in a unity outage probability.

The outage performance versus SNR is shown in plot 500 of FIG. 5 fordifferent values of outage threshold γ_(out). Two cases are shown inplot 500; the case where the interference power scales with SNR and thecase where the interference power is fixed. Plot 500 shows that when theinterference power scales with SNR, the system diversity gain reacheszero and a noise floor appears in all curves of plot 500 due to theeffect of interference on the system performance. On the other hand,when the interference power is fixed, the system performance keepsenhancing as SNR increases. Also, we see from this figure that theoutage threshold is affecting the system behavior through affecting itscoding gain and not the diversity order. the effect of interference onthe system performance. On the other hand, when the interference poweris fixed, the system performance keeps enhancing as SNR increases. Also,we see from this figure that the outage threshold is affecting thesystem behavior through affecting its coding gain and not the diversityorder.

Plot 600 of FIG. 6 shows the outage performance versus SNR for differentnumbers of PU receivers M and different values of interference powers γ_(r) ^(I), γ _(d) ^(I) including the case when they are unequal. Plot600 shows a comparison of the interference severity at the relays anddestination on the system performance. It is obvious from Plot 600 thatthe interference at the relay nodes is more severe on the systembehavior compared to that at the destination node. This is because theinterference at the relays affects the signal on the first hop which isalso affecting the re-encoded signal on the second hop. In other words,the signal processing conducted by the relay nodes is negativelyaffected by the interference, resulting in a further degradation in thesystem performance. Furthermore, the enhancement in system performancedue to having more PU receivers is clear in plot 600. Clearly, thisenhancement in system performance happens in the coding gain and not thediversity order of the system.

The asymptotic behavior of the system is studied in plot 700 of FIG. 7.Two cases are shown in plot 700; a system performance with fulldiversity gain and a system performance with zero diversity gain. Thesystem can achieve full diversity gain only if the interference at therelays and destination is assumed to be fixed and not scaling with SNR.This was summarized in case 1 of the asymptotic analysis. On the otherhand, when the interference at the relays or at the destination or atboth scales with SNR, the system reaches zero diversity gain and a noisefloor appears in the results due to the effect of interference on thesystem performance. Furthermore, it can be seen from plot 700 that theworst performance is achieved when both γ _(r) ^(I), γ _(d) ^(I) scalewith SNR, as expected. Also, the case where γ _(r) ^(I) scales with SNRresults in worse performance compared to the case where γ _(d) ^(I)scales with SNR as the interference at the relays is more severe on thesystem performance compared to that at the destination node. This resultwas also illustrated in FIG. 6.

Plot 800 of FIG. 8 studies the impact of number of PU receivers M on thesystem behavior. It portrays the outage performance versus M fordifferent numbers of relays K. It can be seen from plot 800 that when Mincreases the outage probability decreases, but the slope of the curvesdepends on the value of K. The highest slope is achieved at the largestvalue of K, as expected.

The primary channel selection method for relay networks provides a newscenario in spectrum-sharing opportunistic DF relay networks where thePU receivers are assumed to utilize orthogonal spectrum bands in thepresence of interference from PU transmitter. Closed-form expression wasderived for the outage probability assuming the i.n.i.d. generic case ofrelays second hop channels. Furthermore, the system outage performancewas evaluated at the high SNR regime where simple expressions for theoutage probability, diversity order, and coding gain were derived.Monte-Carlo simulations proved the accuracy of the achieved analyticaland asymptotic results. Main findings illustrated that with fixedinterference power, the diversity order of the secondary system equalsthe number of relays and it is not affected by the number of PUreceivers. Also, results showed that the number of PU receivers affectsthe system performance through affecting the coding gain. Finally,results illustrated that when the interference at the SU relays or theSU destination or at both scales with SNR, the system reaches a zerodiversity gain and a noise floor appears in the results due to theeffect of interference on the system performance.

It is to be understood that the present invention is not limited to theembodiments described above, but encompasses any and all embodimentswithin the scope of the following claims.

We claim:
 1. A primary channel selection method for relay networks,comprising the steps of: selecting among available primary users oneprimary user receiver P_(Sel) whose channel results in a bestperformance for users of a secondary system; sharing the one primaryuser receiver's spectrum with secondary users (source and relay); andrestricting the sharing of the primary user receiver's spectrum bandsonly to the secondary users; wherein the spectrum bands of the primaryuser receivers are orthogonal and the best performance of the secondarysystem is achieved.
 2. The primary channel selection method for relaynetworks according to claim 1, further comprising the steps of asecondary user (SU) S establishing a S→R_(k) link to K relays; and thesecondary user (SU) source S sending its message x to the K relays viathe S→R_(k) link under a transmit power constraint guaranteeing thatinterference with the selected PU receiver P_(Sel) does not exceed athreshold I_(p).
 3. The primary channel selection method for relaynetworks according to claim 2, further comprising the step of thesecondary user (SU) source S calculating the transmit power constraintutilizing a formula characterized by the relation:${P_{S} = \left. {I_{P}\text{/}\begin{matrix}\min \\m\end{matrix}} \middle| g_{s,m} \right|^{2}},$ where P_(S) is the SUsource transmit power, g_(s,m) is a channel coefficient of anS→P_(m)link established during a first communication phase, said SUsource S obtaining said g_(s,m) by either a direct reception of pilotsignals from primary users or by exchange of channel information betweenprimary and secondary users through a band manager.
 4. The primarychannel selection method for relay networks according to claim 3,further comprising the steps of: said multiple relays (R_(k))establishing a R_(k)→D link to a secondary destination D; said multiplerelays (R_(k)) establishing an interfering R_(k)→P_(k) link to thek^(th) primary receiver P_(k); a primary transmitter P_(Tx) establishingan interfering link P_(Tx)→D to the secondary destination D; and eachrelay calculating a first hop SINR representing the received signaltransmitted by S at the k^(th) relay said calculation beingcharacterized by the relation:γ_(S,k)=√{square root over (P _(S))}h _(S,k) x ₀+√{square root over (P_(p) ¹)}f _(p,k) x _(p) +n _(k), where γ_(S,k) is the first hop SINR,h_(S,k) is the channel coefficient of the S→R_(k) link, x₀ is thetransmitted symbol from the SU source S with

{|x₀|²}=P₀, f_(p,k) is the channel coefficient of the P_(Tx)→R_(k) link,x_(p) is the transmitted symbol from the PU transmitter P_(Tx) with{|x_(p)|²} = P_(p)¹, where the superscript 1 is used to denote thatthis is the transmitted power at a first communication phase, n_(k)˜

(0, N₀) being noise in the communication links,

{•} denoting an expectation operation.
 5. The primary channel selectionmethod for relay networks according to claim 4, further comprising thestep of selecting active relays, said active relays being defined as therelays whose received signal is at least as strong as an outagethreshold γ_(out); wherein a signal-to-interference-plus-noise ratio(SINR) at the k^(th) relay is characterized by the relation:${\gamma_{s,k} = {\frac{\frac{I_{p}}{N_{O}}\frac{\left| h_{s,k} \right|^{2}}{W_{1}}}{\left. \frac{P_{p}^{1}}{N_{O}} \middle| f_{p,k} \middle| {}_{2}{+ 1} \right.} = {\frac{X_{s,k}}{Y_{1} + 1} = \frac{X_{s,k}}{Z_{1}}}}},$where ${W_{1} = \left. \begin{matrix}\min \\m\end{matrix} \middle| g_{s,m} \right|^{2}},$ X_(s,k), Y₁, and Z₁ arefirst communication phase random variables (RVs) used herein.
 6. Theprimary channel selection method for relay networks according to claim5, further comprising the step of identifying a decoding set C_(L) ofthe active relays, said C_(L) being defined as the set of active relaysthat could have correctly decoded the source message upon initialestablishment of the R_(k)→D link and being characterized by therelation: $\begin{matrix}{C_{L}\overset{\Delta}{=}\left\{ {k \in {{S_{r}\text{:}\frac{1}{2}{\log_{2}\left( {1 + \gamma_{S,k}} \right)}} \geq R}} \right\}} \\{{= \left\{ {k \in {{S_{r}\text{:}\gamma_{S,k}} \geq {2^{2R} - 1}}} \right\}},}\end{matrix}$ where S_(r) is a set of L relays and R denotes a fixedspectral efficiency threshold.
 7. The primary channel selection methodfor relay networks according to claim 6, further comprising the step ofsaid decoding set C_(L) of the active relays estimating channelcoefficients g_(l,m) subject to the PU interference constraint and atransmit power at a relay R_(l) of the decoding set C_(L), the R_(l)transmit power being characterized by the relation:${P_{R_{l}} = \left. {I_{p}\text{/}\begin{matrix}\min \\m\end{matrix}} \middle| g_{l,m} \right|^{2}};{and}$ said decoding setC_(L) of the active relays sending a training sequence to the secondarydestination D at said R_(l) transmit power.
 8. The primary channelselection method for relay networks according to claim 7, furthercomprising the steps of: the secondary destination D calculating amaximum X_(l,d) based on a signal-plus-noise ratio (SINR) at thesecondary destination D resulting from the l^(th) relay signal said SINRbeing characterized by the relation:${\gamma_{l,d} = {\frac{\frac{I_{p}}{N_{O}}\frac{\left| h_{l,d} \right|^{2}}{W_{2}}}{\left. \frac{P_{p}^{2}}{N_{O}} \middle| f_{p,d} \middle| {}_{2}{+ 1} \right.} = {\frac{X_{l,d}}{Y_{2} + 1} = \frac{X_{l,d}}{Z_{2}}}}},$where P_(p) ² is the transmitted power of the interferer at a secondcommunication phase, ${W_{2} = \left. \begin{matrix}\min \\m\end{matrix} \middle| g_{l,m} \right|^{2}},X_{l,d},$ Y₂, and Z₂ aresecond communication phase RVs used herein, X_(l,d) is thesignal-to-noise ratio (SNR) received from the relays; and the secondarydestination D sending a positive acknowledge signal to the relay havingthe maximum X_(l,d).
 9. The primary channel selection method for relaynetworks according to claim 8, further comprising the step of said relaywith the maximum X_(l,d) forwarding said message x from said SU source Sto said secondary destination D.
 10. The primary channel selectionmethod for relay networks according to claim 9, further comprising thestep of coordinating the training sequences transmitted by the relays totransmit in a time-division duplex manner.
 11. A computer softwareproduct, comprising a non-transitory medium readable by a processor, thenon-transitory medium having stored thereon a set of instructions forperforming a primary channel selection method for relay networks, theset of instructions including: (a) a first sequence of instructionswhich, when executed by the processor, causes said processor to selectamong available primary users one primary user receiver P_(Sel) whosechannel results in a best performance for users of a secondary system;(b) a second sequence of instructions which, when executed by theprocessor, causes said processor to share the one primary userreceiver's spectrum with secondary users (source and relay); and (c) athird sequence of instructions which, when executed by the processor,causes said processor to restrict the sharing of the primary userreceiver's spectrum bands only to the secondary users; wherein thespectrum bands of the primary user receivers are orthogonal and the bestperformance of the secondary system is achieved.
 12. The computersoftware product according to claim 11, further comprising: a fourthsequence of instructions which, when executed by the processor, causessaid processor to utilize a secondary user (SU) S to establish a S→R_(k)link to K relays; and a fifth sequence of instructions which, whenexecuted by the processor, causes said processor to utilize thesecondary user (SU) source S to send its message x to the K relays viathe S→R_(k) link under a transmit power constraint which guarantees thatinterference with the selected PU receiver P_(Sel) does not exceed athreshold I_(p).
 13. The computer software product according to claim12, further comprising: a sixth sequence of instructions which, whenexecuted by the processor, causes said processor to calculate thetransmit power constraint for the secondary user (SU) source S utilizinga formula characterized by the relation:${P_{S} = \left. {I_{p}\text{/}\begin{matrix}\min \\m\end{matrix}} \middle| g_{s,m} \right|^{2}},$ where g_(s,m) is achannel coefficient of an S→P_(m) link established during a firstcommunication phase, said SU source S obtaining said g_(s,m) by either adirect reception of pilot signals from primary users or by exchange ofchannel information between primary and secondary users through a bandmanager.
 14. The computer software product according to claim 13,further comprising: a seventh sequence of instructions which, whenexecuted by the processor, causes said processor to establish a R_(k)→Dlink from said multiple relays (R_(k)) to a secondary destination D; aneighth sequence of instructions which, when executed by the processor,causes said processor to establish an interfering R_(k)→P_(k) link fromsaid multiple relays (R_(k)) to the k^(th) primary receiver P_(k); aninth sequence of instructions which, when executed by the processor,causes said processor to establish an interfering link P_(Tx)→D from aprimary transmitter P_(Tx) to the secondary destination D; and a tenthsequence of instructions which, when executed by the processor, causessaid processor to, for each relay, calculate a first hop SINRrepresenting the received signal transmitted by S at the k^(th) relaysaid calculation being characterized by the relation:γ_(S,k)=√{square root over (P _(S))}h _(S,k) x ₀+√{square root over (P_(p) ¹)}f _(p,k) x _(p) +n _(k), where γ_(S,k) is the first hop SINR,h_(S,k) is the channel coefficient of the S→R_(k) link, x₀ is thetransmitted symbol from the SU source S with

{|x₀|²}=P₀, f_(p,k) is the channel coefficient of the P_(Tx)→R_(k) link,x_(p) is the transmitted symbol from the PU transmitter P_(Tx) with{|x_(p)|²}=P_(p) ¹, where the superscript 1 is used to denote that thisis the transmitted power at a first communication phase, n_(k)≈

(0, N₀) being noise in the communication links,

{•} denoting an expectation operation.
 15. The computer software productaccording to claim 14, further comprising: an eleventh sequence ofinstructions which, when executed by the processor, causes saidprocessor to select active relays, said active relays being defined asthe relays whose received signal is at least as strong as an outagethreshold γ_(out); and wherein a signal-to-interference-plus-noise ratio(SINR) at the k^(th) relay is characterized by the relation:${\gamma_{s,k} = {\frac{\frac{I_{p}}{N_{O}}\frac{\left| h_{s,k} \right|^{2}}{W_{1}}}{\left. \frac{P_{p}^{1}}{N_{O}} \middle| f_{p,k} \middle| {}_{2}{+ 1} \right.} = {\frac{X_{s,k}}{Y_{1} + 1} = \frac{X_{s,k}}{Z_{1}}}}},$where ${W_{1} = \left. \begin{matrix}\min \\m\end{matrix} \middle| g_{s,m} \right|^{2}},X_{s,k},Y_{1},$ and Z₁ arefirst communication phase RVs used herein.
 16. The computer softwareproduct according to claim 15, further comprising: a twelfth sequence ofinstructions which, when executed by the processor, causes saidprocessor to identify a decoding set C_(L) of the active relays, saidC_(L) being defined as the set of active relays that could havecorrectly decoded the source message upon initial establishment of theR_(k)→D link and being characterized by the relation: $\begin{matrix}{C_{L}\overset{\Delta}{=}\left\{ {k \in {{S_{r}\text{:}\frac{1}{2}{\log_{2}\left( {1 + \gamma_{S,k}} \right)}} \geq R}} \right\}} \\{{= \left\{ {k \in {{S_{r}\text{:}\gamma_{S,k}} \geq {2^{2R} - 1}}} \right\}},}\end{matrix}$ where S_(r) is a set of L relays and R denotes a fixedspectral efficiency threshold.
 17. The computer software productaccording to claim 16, further comprising: a thirteenth sequence ofinstructions which, when executed by the processor, causes saidprocessor to have said decoding set C_(L) of the active relays estimateg_(l,m) subject to the PU interference constraint and a transmit powerat an at R_(l) of the decoding set C_(L), the R_(l) transmit power beingcharacterized by the relation:${P_{R_{l}} = \left. {I_{p}\text{/}\begin{matrix}\min \\m\end{matrix}} \middle| g_{l,m} \right|^{2}};$ and a fourteenth sequenceof instructions which, when executed by the processor, causes saidprocessor to have said decoding set C_(L) of the active relays send atraining sequence to the secondary destination D at said R_(l) transmitpower.
 18. The computer software product according to claim 17, furthercomprising: a fifteenth sequence of instructions which, when executed bythe processor, causes said processor to have the secondary destination Dcalculate a maximum X_(l,d) based on a signal-plus-noise ratio (SINR) atthe secondary destination D resulting from the l^(th) relay signal saidSINR being characterized by the relation:${\gamma_{l,d} = {\frac{\frac{I_{p}}{N_{O}}\frac{\left| h_{l,d} \right|^{2}}{W_{2}}}{\left. \frac{P_{p}^{2}}{N_{O}} \middle| f_{p,d} \middle| {}_{2}{+ 1} \right.} = {\frac{X_{l,d}}{Y_{2} + 1} = \frac{X_{l,d}}{Z_{2}}}}},$where P_(p) ² is the transmitted power of the interferer at a secondcommunication phase, ${W_{2} = \left. \begin{matrix}\min \\m\end{matrix} \middle| g_{l,m} \right|^{2}},X_{l,d},$ Y₂, and Z₂ aresecond communication phase RVs used herein, X_(l,d) is thesignal-to-noise ratio (SNR) received from the relays; and a sixteenthsequence of instructions which, when executed by the processor, causessaid processor to have the secondary destination D send a positiveacknowledge signal to the relay having the maximum X_(l,d).
 19. Thecomputer software product according to claim 18, further comprising aseventeenth sequence of instructions which, when executed by theprocessor, causes said processor to have said relay with the maximumX_(l,d) forward said message x from said SU source S to said secondarydestination D.
 20. The computer software product according to claim 19,further comprising an eighteenth sequence of instructions which, whenexecuted by the processor, causes said processor to coordinate thetraining sequences transmitted by the relays to transmit in atime-division duplex manner.